Question

A solid sphere of radius 3 cm is melted and then recast into small spherical balls each of diameter 0.6 cm. Find the number of small balls thus obtained.
Please answer soon, need it urgently for exam preparation!!!!

Answer 1

radius of bigger sphere(R) = 3 cm
radius of smaller balls(r) = 0.6/2 = 0.3 cm
let the number of small balls = n

n×volume of a small balls = volume of bigger sphere

$n\times \frac{4}{3} \pi r^3= \frac{4}{3} \pi R^3\\ \\ \Rightarrow n= \frac{R^3}{r^3} \\ \\\Rightarrow n= (\frac{R}{r} )^3=(\frac{3}{0.3} )^3=10^3\\ \\ \Rightarrow n=\boxed{1000}$

Number of small balls is 1000.

Answer 2

Radius of bigger sphere(R)-3cm Radius of smaller sphere(r)-0.3cm No. Of smaller sphere obtained=volume of bigger sphere/volume of smaller sphere =4/3πR×R×R/4/3πr×r×r =R×R×R/r×r×r =3×3×3/0.3×0.3×0.3 =1000 balls